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Edgeworth expansion of random weighting estimation in semi-parametric regression models. (Chinese. English summary) Zbl 1073.62039

Summary: In order to avoid the compulsory resampling bootstrap method when parameter estimation is performed in a simple semiparametric regression model \(y=x\beta+g(t)+\varepsilon\), a least squares random weighting estimation quantity \(\widetilde\lambda_n\) concerned with the parameter \(\beta\) was constructed by using a random weighting method. The Edgeworth expansion of the \(\widetilde \lambda_n\) distribution was obtained with convergence speed of order of \(O(n^{-1/2})\).

MSC:

62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics
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